A Study to Assess the Safety, Tolerability, and Effect on Disease Progression of BIIB105 in Participants With Amyotrophic Lateral Sclerosis (ALS) and Participants With the ALS Ataxin-2 (ATXN2) Genetic Mutation

Key Inclusion Criteria: Part 1: * Ability of the participant to understand the purpose and risks of the study and indicate informed consent, and the ability of the participant or the participant's legally authorized representative, to provide signed and dated informed consent and authorization to use protected health information in accordance with national and local privacy regulations. * No known presence or family history of mutations in the superoxide dismutase 1 (SOD1) or fused in sarcoma (FUS) genes. * Participants in Cohorts A, B, C1 and D1, must meet the laboratory-supported probable, probable, or definite criteria for diagnosing ALS according to the World Federation of Neurology El Escorial criteria (revised according to the Airlie House Conference 1998 \[Brooks 2000\]). Participants in Cohort C2 and D2, must meet any of the prior conditions, but may also only meet clinically possible criteria for diagnosing ALS, or exhibit weakness attributable to ALS in the presence of ataxin-2 protein (ATXN2) intermediate repeats. * In participants in Cohorts C2 and D2, confirmed intermediate cytosine-adenine-guanine/cytosine-adenine-adenine (CAG/CAA) repeat expansion in the ataxin-2 (ATXN2) gene as defined by at least 1 allele carrying 30 to 33 CAG/CAA repeats. * Slow vital capacity (SVC) criteria: * In participants in Cohorts A, B, C1, and D1, SVC ≥60% of predicted value as adjusted for sex, age, and height (from the sitting position). * In participants in Cohort C2 and D2, SVC ≥50% of predicted value as adjusted for sex, age, and height (from the sitting position). * If taking riluzole, participant must be on a stable dose for ≥30 days prior to Day 1 and expected to remain at that dose until the final study visit, unless the Investigator determines that it should be discontinued for medical reasons, in which case it may not be restarted during the study. * Participants taking concomitant edaravone at study entry must be on a stable dose for ≥60 days prior to the first dose of study treatment (Day 1). Participants taking concomitant edaravone must be willing to continue with the same dose regimen throughout the study, unless the Investigator determines that edaravone should be discontinued for medical reasons, in which case it may not be restarted during the study. Edaravone may not be administered on dosing days of this study. * Screening values of coagulation parameters including platelet count, international normalized ratio (INR), prothrombin time (PT), and activated partial thromboplastin time (aPTT) should be within normal ranges. * Has an informant/caregiver who, in the Investigator's judgment, has frequent and sufficient contact with the participant as to be able to provide accurate information about the participant's cognitive and functional abilities at screening. Part 2: * Ability of the participant to understand the purpose and risks of the study and indicate informed consent, and the ability of the participant or the participant's legally authorized representative to provide signed and dated informed consent and authorization to use protected health information in accordance with national and local privacy regulations * Participants must have completed Study NCT04494256 Part 1 through Week 25 (Day 175 Visit for Cohorts A, B, C1, C2; Day 176 Visit for Cohorts D1, D2). This inclusion criterion does not apply to a participant if Part 1 was terminated by the Sponsor before the participant reached Week 25. * Participants from Cohorts A, B, C1, and C2 must have a washout of ≥16 weeks between the last dose of study treatment received in Study NCT04494256 Part 1 and the first dose of BIIB105 received in Study NCT04494256 Part 2. Participants from Cohorts D1 and D2 do not require a washout period. * If taking riluzole, participant must be on a stable dose for ≥30 days prior to Day 1 and expected to remain at that dose until the final study visit, unless the Investigator determines that it should be discontinued for medical reasons, in which case it may not be restarted during the study. * Participants taking concomitant edaravone at study entry must be on a stable dose for ≥60 days prior to the first dose of study treatment (Day 1). Participants taking concomitant edaravone must be willing to continue with the same dose regimen throughout the study, unless the Investigator determines that edaravone should be discontinued for medical reasons, in which case it may not be restarted during the study. Edaravone may not be administered on dosing days of this study. * Screening values of coagulation parameters including platelet count, INR, PT, and aPTT should be within normal ranges. Key Exclusion Criteria Part 1: * History or positive test result at Screening for human immunodeficiency virus (HIV). * Current hepatitis C infection. * Current hepatitis B infection. * History of alcohol or substance abuse ≤6 months of Screening that would limit participation in the study, as determined by the Investigator. * Current or anticipated need, in the opinion of the Investigator, of a diaphragm pacing system during the study period. * Presence of tracheostomy. * In participants from Cohorts A, B, C1, and D1, history of myocardial infarction, as determined by the Investigator. * In participants from Cohorts A, B, C1, and D1, poorly controlled type 1 or 2 diabetes mellitus defined as hemoglobin A1c (HbA1c) ≥8% during Screening. * In participants in Cohorts A, B, and C1, prescreening ALSFRS-R slope \>-0.4 points/month, where prescreening ALSFRS-R slope is defined as: (ALSFRS-R score at Screening - 48) / (months from date of symptom onset to date of Screening). This criterion is not applicable for Cohorts C2, D1, and D2. * Treatment with another investigational drug (including investigational drugs for ALS through compassionate use programs) or biological agent within 1 month or 5 half-lives of study agent, whichever is longer, before Screening. * Treatment with an approved disease-modifying therapy for ALS other than riluzole or edaravone within 1 month or 5 half-lives of therapy, whichever is longer, before completion of screening. * Treatment with an antiplatelet or anticoagulant therapy that cannot safely be interrupted for lumbar puncture (LP) according to local standard of care and/or institutional guidelines, in the opinion of the Investigator or Prescriber. * Female participants who are pregnant or currently breastfeeding and those intending to become pregnant during the study. Part 2: * History or positive test result at Screening for HIV. If participants from Cohorts D1 and D2 who would seamlessly roll from Part 1 into Part 2 test positive for HIV during screening for Part 2 but are clinically asymptomatic, they may enroll in Part 2 at the discretion of the Investigator. * Current hepatitis C infection. If participants from Cohorts D1 and D2 who would seamlessly roll from Part 1 into Part 2 test positive for hepatitis C during screening for Part 2 but are clinically asymptomatic, they may enroll in Part 2 at the discretion of the Investigator. * Current hepatitis B infection. If participants from Cohorts D1 and D2 who would seamlessly roll from Part 1 into Part 2 test positive for hepatitis B during screening for Part 2 but are clinically asymptomatic, they may enroll in Part 2 at the discretion of the Investigator. * History of alcohol or substance abuse ≤ 6 months of Screening that would limit participation in the study, as determined by the Investigator. * Current or anticipated need, in the opinion of the Investigator, of a diaphragm pacing system during the study period. * In participants from Cohorts A, B, C1, and D1, history of myocardial infarction, as determined by the Investigator. * In participants from Cohorts A, B, C1, and D1, poorly controlled type 1 or 2 diabetes mellitus defined as HbA1c ≥8% during Screening. * Treatment with another investigational drug (including investigational drugs for ALS through compassionate use programs; excluding BIIB105) or biological agent within 1 month or 5 half-lives of study agent, whichever is longer, before Screening. * Treatment with an antiplatelet or anticoagulant therapy that cannot safely be interrupted for LP according to local standard of care and/or institutional guidelines, in the opinion of the Investigator or Prescriber. * Female participants who are pregnant or currently breastfeeding and those intending to become pregnant during the study. NOTE: Other protocol defined Inclusion/Exclusion criteria may apply.